Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2002
|
| Series: | Memoirs of the American Mathematical Society
752 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 158, number 752 (third of 4 numbers)." |
| Physical Description: | XV, 114 S. graph. Darst. |
| ISBN: | 0821829068 |
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| 245 | 1 | 0 | |a Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces |c Linus Kramer |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2002 | |
| 300 | |a XV, 114 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction x
Chapter 1. The Leray Serre spectral sequence 1
l.A. Additive structure 2
l.B. Multiplicative structure 6
l.C. Notes on collapsing 9
Chapter 2. Ranks of homotopy groups 11
2.A. The Whitehead tower 11
2.B. The Cartan Serre Theorem 15
Chapter 3. Some homogeneous spaces 18
3.A. Structure of compact Lie groups 18
3.B. Certain homogeneous spaces 21
3.C. The integral classification 28
Chapter 4. Representations of compact Lie groups 33
4.A. The classification of irreducible representations 33
4.B. Subgroups of classical groups 35
4.C. Useful formulas 36
4.D. The Dynkin index 49
Chapter 5. The case when G is simple 51
5.A. Case (I): H*(X) = / z{u, v). 51
5.B. Case (II): H*(X) = Z[a]/{a2) ® / z(w). 57
Chapter 6. The case when G is semisimple 63
6.A. The split case 63
6.B. The non split case (I): H*(X) =/ z(u,v). 67
6.C. The non split case (II): W(X) = 1[a}/(a2) g f z(w). 72
Chapter 7. Homogeneous compact quadrangles 75
7.A. Generalized quadrangles and group actions 77
7.B. Compact quadrangles 79
7.C. Some results about compact transformation groups 83
7.D. Group actions on compact quadrangles 85
7.E. The Stiefel manifolds 87
7.F. The (4, An 5) series 90
7.G. Products of spheres 91
7.H. Summary 92
Chapter 8. Homogeneous focal manifolds 94
vii
viii CONTENTS
8.A. Isoparametric hypersurfaces 96
8.B. The Stiefel manifolds 100
8.C. Some sporadic cases 101
8.D. The semisimple case 102
8.E. The (4, in 5) and the (3,4n 4) series 104
8.F. Summary 107
Bibliography 110
|
| any_adam_object | 1 |
| author | Kramer, Linus 1964- |
| author_GND | (DE-588)1145894054 |
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| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512/.2 510 |
| dewey-search | 512/.2 510 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014410864 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:02:27Z |
| institution | BVB |
| isbn | 0821829068 |
| language | English |
| lccn | 2002018395 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009856302 |
| oclc_num | 49283943 |
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| physical | XV, 114 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Kramer, Linus 1964- Verfasser (DE-588)1145894054 aut Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces Linus Kramer Providence, RI American Mathematical Society 2002 XV, 114 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 752 "Volume 158, number 752 (third of 4 numbers)." Differentiaalmeetkunde gtt Topologische ruimten gtt Buildings (Group theory) Finite generalized quadrangles Global differential geometry Homogeneous spaces Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gebäude Mathematik (DE-588)4123258-6 gnd rswk-swf Globale Differentialgeometrie (DE-588)4021286-5 gnd rswk-swf Homogener Raum (DE-588)4025787-3 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s DE-604 Homogener Raum (DE-588)4025787-3 s Globale Differentialgeometrie (DE-588)4021286-5 s Gebäude Mathematik (DE-588)4123258-6 s Memoirs of the American Mathematical Society 752 (DE-604)BV008000141 752 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009856302&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kramer, Linus 1964- Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces Memoirs of the American Mathematical Society Differentiaalmeetkunde gtt Topologische ruimten gtt Buildings (Group theory) Finite generalized quadrangles Global differential geometry Homogeneous spaces Gruppentheorie (DE-588)4072157-7 gnd Gebäude Mathematik (DE-588)4123258-6 gnd Globale Differentialgeometrie (DE-588)4021286-5 gnd Homogener Raum (DE-588)4025787-3 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4123258-6 (DE-588)4021286-5 (DE-588)4025787-3 |
| title | Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces |
| title_auth | Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces |
| title_exact_search | Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces |
| title_full | Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces Linus Kramer |
| title_fullStr | Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces Linus Kramer |
| title_full_unstemmed | Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces Linus Kramer |
| title_short | Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces |
| title_sort | homogeneous spaces tits buildings and isoparametric hypersurfaces |
| topic | Differentiaalmeetkunde gtt Topologische ruimten gtt Buildings (Group theory) Finite generalized quadrangles Global differential geometry Homogeneous spaces Gruppentheorie (DE-588)4072157-7 gnd Gebäude Mathematik (DE-588)4123258-6 gnd Globale Differentialgeometrie (DE-588)4021286-5 gnd Homogener Raum (DE-588)4025787-3 gnd |
| topic_facet | Differentiaalmeetkunde Topologische ruimten Buildings (Group theory) Finite generalized quadrangles Global differential geometry Homogeneous spaces Gruppentheorie Gebäude Mathematik Globale Differentialgeometrie Homogener Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009856302&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT kramerlinus homogeneousspacestitsbuildingsandisoparametrichypersurfaces |